Question

Find the expected value, μ, and standard deviation, σ, for a binomial random variable with each of the following values of n and p. (Round all answers for σ to four decimal places.) (a) n = 50, p = 1/2. μ = σ =

(b) n = 300, p = 1/4. μ = σ =

(c) n = 1000, p = 1/5. μ = σ =

(d) n = 1, p = 0.3. μ = σ =

(e) n = 20, p = 2/5. μ = σ =

Answer 1

Ans:

We know that

mean, $\mu$ =np

standard deviation, $\sigma$ =sqrt(np(1-p))

e.g. for a)n=50,p=0.5

mean=np=50*0.5=25

standard deviation=sqrt(50*0.5*0.5)=3.5355

	n	p	mean	std. dev.
a	50	0.5	25	3.5355
b	300	0.25	75	7.5000
c	1000	0.2	200	12.6491
d	1	0.3	0.3	0.4583
e	20	0.4	8	2.1909